Enveloping for multilink communications

ABSTRACT

A communications system between a source and a destination includes a transmitter at the source and a communication connectivity. The transmitter comprises a preprocessor and a candidate envelope folder to provide M known a priori digital envelopes, M≥1. The preprocessor has N input ports and N output ports, N&gt;M, performs at least one wavefront multiplexing (WFM) transform on N inputs received at the N input ports to generate N outputs at the N output ports. The preprocessor performs the at least one WFM transform by calculating, for each of the N outputs, a linear combination of the N inputs using one of the M digital envelopes such that a digital format of one of the N outputs appears to human sensors as having features substantially identical to a digital format of the one of the M digital envelopes.

RELATED APPLICATIONS

This application is a continuation of application Ser. No. 14/993,397,entitled “Enveloping for Multilink Communications”, filed on Jan. 12,2016, and is related to incoherent wavefront multiplexing (WF muxing)and incoherent wavefront demultiplexing (WF demuxing) techniques in thefollowing references:

-   -   1. U.S. Pat. App. Pub. No. 20150032706 A1; “Enveloping for Cloud        Computing via Wavefront Muxing,” pub. on Jan. 29, 2015.    -   2. U.S. Pat. App. Pub. No. 20150040184 A1, “Digital Enveloping        for Digital Right Management and Re-broadcasting,” pub. on Feb.        5, 2015.    -   3. U.S. Pat. App. Pub. No. 20110197740; “Novel Karaoke and        Multi-Channel Data Recording/Transmission Techniques via        Wavefront Multiplexing and Demultiplexing,” pub. on Aug. 18,        2011.    -   4. U.S. Pat. App. Pub. No. 20130333544; “Novel Karaoke and        Multi-Channel Data Recording/Transmission Techniques via        Wavefront Multiplexing and Demultiplexing,” pub. on Dec. 19,        2013.    -   5. U.S. Pat. App. Pub. No. US 20140081989; “WF Muxing and        Demuxing for Cloud Data Storage and Transport,” pub. on Mar. 20,        2014.    -   6. U.S. Pat. Appl. Pub. No. 20150248431; “Survivable Cloud Data        Storage and Transport,” published on Sep. 3, 2015.        All of the above applications are incorporated herein by        reference in their entireties.

This application is also related to satellite communications usingmultiple transponders, deployed UAVs, or others via coherent wavefrontmultiplexing (WF muxing) and wavefront demultiplexing (WF demuxing)techniques in the following references:

-   -   1. U.S. Pat. No. 8,111,646 B1; “Communication system for        dynamically combining power from a plurality of propagation        channels in order to improve power levels of transmitted signals        without affecting receiver and propagation segments,” issued on        Feb. 7, 2012.    -   2. U.S. Pat. No. 8,547,897 B2; “Coherent power combining for        signals through multiple satellite communications channels,”        issued on Oct. 1, 2013.    -   3. U.S. Pat. No. 8,538,326 B2; “Accessing LP transponders with        CP terminals via wavefront multiplexing techniques,” issued on        Sep. 17, 2013.    -   4. U.S. Pat. App. Pub. No. 20140161018 A1; “Multi-user MIMO via        frequency re-use in smart antenna,” pub. on Jun. 12, 2014.    -   5. U.S. Pat. App. Pub. No. 2014/0219124, “Multi-user MIMO via        active scattering platforms,” pub. on Aug. 7, 2014.    -   6. U.S. Pat. No. 8,953,728 B2, “Systems for processing data        streams,” issued on Feb. 10, 2015.        All of the above are incorporated herein by reference in their        entireties.

BACKGROUND Field of the Disclosure

There are needs for better privacy protection on data transport.Enveloping techniques using incoherent WF muxing will enhance privacyprotection on data communications. The disclosure relates to methods andarchitectures of packing or enveloping data using Wavefront multiplexing(WF muxing) for transport via multiple communication links. It isfocused to appearance of data package/envelope and reliability ofenclosed data. The WF muxing implemented on information digital streambefore modulation in radiation chains in a transmitter shall provideenhanced data privacy and better availability in multiple-linkcommunications between an information source and an informationdestination. The WF multiplexed (WF muxed) information data streams in asource will be individually and concurrently sent via the multiple linksaccordingly for information data transport to a destination. The relatedWF demuxing will be performed on information digital streams afterdemodulation in receiving chains in a corresponding receiver.

We use the terms of information data or digital information streams todifferentiate the data signals or digital signal streams. In atransmission chain, information data will usually be modulated bymodulators into data signals before transmission. Similarly in areceiving chain, a received digital signal stream will be demodulated bydemodulators and converted into a digital information stream. Theincoherent WF muxing/demuxing will be used for processing informationdata or digital information streams for the benefits of enhanced privacyand better availability. On the other hand, the coherent WFmuxing/demuxing for processing data signals or digital signal streamswill be used for power combining and/or dynamic resource allocations forcommunications channels.

This invention application addresses enhanced privacy, and betterreliability (or availability) of data transports in communications withmulti-links; such as concurrently via multiple satellites, airborneplatforms, wireless terrestrial links, and/or other wireless links. Themulti-link communications may include the use of cloud transport ofmultiple WF-muxed data packages.

Many of the data may be image or audio related. Since multiple data setsto be transported will be preprocessed on client sides, each of thetransported data is a multiplexed (muxed) data set individually which isunintelligible by itself. Therefore, the proposed approaches shallremove the concerns on information leaks from individual communicationslinks, or those on the rights or ownerships of stored/transported datathrough individual communications links. Digital images will be used toexemplify the digital enveloping/de-enveloping techniques in this patentapplication. Other types of digital streams may be easily incorporatedas the digital envelopes for the proposed enveloping techniques.

Embodiments of “writing” and “reading” processes will be summarized andpresented concisely. “Writing” features a process on multiple originalimages concurrently via WF muxing transformations, generating WF muxeddata before transmitting. A “reading” process corresponds to a WFdemuxing transformation on WF muxed data stored on cloud, reconstitutingoriginal data sets. The enveloping is a subset of “writing” proceduresunder constraints that enveloped messages, or products of the writingprocedures, shall preserve some desired features in digital appearance,and the de-enveloping is a subset of reading procedures to reconstituteembedded mails from the enveloped messages.

SUMMARY

Wavefront multiplexing/demultiplexing (WF muxing/demuxing) processfeatures an algorithm invented by Spatial Digital Systems (SDS) forsatellite communications where transmissions demand a high degree ofpower combining, security, reliability, and optimization. WFmuxing/demuxing, embodying an architecture that utilizesmulti-dimensional transmissions, has found applications in fields beyondthe satellite communication domain. One such application is datatransport/storage on cloud where privacy, data integrity, and redundancyare important. Enveloping and de-enveloping on digital data may be usedfor both data transport and data storage. We will use data transport viawireless links to exemplify the concept of enveloping and de-envelopingfor digital information data.

Privacy are important concerns on data transport, especially in wirelesscommunications including those via transponding satellites, airplatforms and unmanned aerial vehicles (UAVs). Wavefrontmultiplexing/demultiplexing (WF muxing/demuxing) process embodies anarchitecture that utilizes multi-dimensional waveforms in data transportover multiple links. Multiple data sets are preprocessed by WF muxingbefore being transported. WF muxed data is aggregated data from multipleinput data sets that have been “customized and processed” anddisassembled into any scalable number of sets of processed data inoutput, with each set being transported via a propagation link orchannel. The original data is reassembled via WF demuxing afterretrieving a lesser but scalable number of WF muxed data sets from themultiple links. In short, the WF muxed data transport solution enhancesdata privacy and data availability via redundancy by, respectively,creating a new dimension to existing security or data privacy methodsand significantly reducing the transported data packages needed forbetter availability via data redundancy formats. In addition, WFmuxing/demuxing methods enable a monitoring capability on the integrityof transported data.

K-space is a well understood term in solid state physics and imagingprocessing. The k-space can refer to:

-   a. Another name for the frequency domain but referring to a spatial    rather than temporal frequency.-   b. Reciprocal space for the Fourier transform of a spatial function.-   c. Momentum space for the vector space of possible values of    momentum for a particle.-   d. According to Wikipedia (September 2015), the k-space in magnetic    resonance imaging (MRI):    -   i. a formalism of k-space widely used in magnetic resonance        imaging (MRI) introduced in 1979 by Likes and in 1983 by        Ljunggren and Twieg.    -   ii. In MRI physics, k-space is the 2D or 3D Fourier transform of        the MR image measured.

We shall introduce the terms K-mux, Kmux, or KMx for representing theWavefront multiplex; and K-muxing, Kmuxing, or KMxing for the Wavefrontmultiplexing. We may use “K-Muxing in satellite communications” for“WF-Muxing in satellite communications”, “K-muxer” for “WF muxer”, andso on. In Electromagnetic (EM) theory, the letter K is often used torepresent a directional vector and is a wave number in a propagationdirection. The term (ωt−{right arrow over (K)}·{right arrow over (R)})has been used extensively for propagation phase. {right arrow over (K)}represents a directional (moving) surface and {right arrow over (R)} adirectional propagation displacement. Both are vectors. Therefore, avector K represents a “wavefront” mathematically. We will be usingk-space as wavefront domain or wavefront space.

This invention of “enveloping” is about to send not all but a portion ofK-muxed data streams through multiple links to destinations. Envelopeddata streams are data sub-files or multiple files K-muxed with a knowndata file as an envelope which may be a sender's personal pictureindicating who is sending the enveloped (embedded) data streams.Different envelopes may feature various pictures of sender's indicating,for instance, sender's mood while sending the enveloped data. Thedigital envelopes may be an old digital video clip for delivering newdigital data streams for communications among family members only. Allfamily members shall have access to the original old video clip.

WF muxing/demuxing for enveloping are configured to use additional knowndigital data streams for probing, authentications and identifications. Amethod for enveloping and then sending data through multiple linkscomprises: (1) transforming multiple first data sets via K-muxing intomultiple enveloped second data sets at a transmitting side, wherein oneof said enveloped second data sets comprises a weighted sum of saidfirst data sets at said transmitting side; (2) sending said envelopedsecond data sets via multiple links to a destination, (3) receiving theenveloped second data sets in the destinations and (4) reconstitutingthe original first data sets via a corresponding K-demuxing operation.

A data processing method comprises: transforming multiple first datasets and a known data set into multiple enveloped second data sets at atransmitting side, wherein one of said enveloped second data setscomprises a weighted sum of said first data sets; and recovering a thirddata sets from some of said enveloped second data sets and said knowndata set at a receiving side, wherein one of said third data setscomprises a weighted sum of said some of said enveloped second datasets.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings disclose illustrative embodiments of the presentdisclosure. They do not set forth all embodiments. Other embodiments maybe used in addition or instead. Details that may be apparent orunnecessary may be omitted to save space or for more effectiveillustration. Conversely, some embodiments may be practiced without allof the details that are disclosed. When the same reference number orreference indicator appears in different drawings, it may refer to thesame or like components or steps.

Aspects of the disclosure may be more fully understood from thefollowing description when read together with the accompanying drawings,which are to be regarded as illustrative in nature, and not as limiting.The drawings are not necessarily to scale, emphasis instead being placedon the principles of the disclosure.

FIG. 1 , a replicate of FIG. 1 in US Patent Application Publication No.US 2015/0032706 A1, depicts a block diagram on “sealing” a digitalenvelope for an embedded digital file via a 2-to-2 WF muxing processorby a sender at a source, sending only one of the two outputs as thedigitally enveloped data to a destination via cloud, and “de-enveloping”the digital envelope and recovering the embedded data in accordance tosome embodiments of this invention. The digital envelope is chosen bythe sender from one of the known candidate digital envelopes to both thesender at the source and the receiver at the destination. The sealingand opening (or un-sealing) process for an envelope are also referred asenveloping and de-enveloping, respectively.

FIG. 1A depicts the same digital enveloping and de-enveloping processes,except the communications between the source and the destination arethrough a satellite link according to embodiments of this invention.

FIG. 2 depicts a block diagram on “sealing” digital envelopes for anembedded digital file via a K-muxing processor by a sender at a source,sending all 4 outputs as the digitally enveloped data to a destinationvia multiple satellites, and “de-enveloping” the digital envelope andrecovering the embedded data in accordance to embodiments of thisinvention.

FIG. 2A depicts a block diagram on digital enveloping for 4 K-muxeddigital files by a sender at a source, sending 4 independent digitallyenveloped outputs to a destination via multiple satellites, according tosome embodiments of this invention.

FIG. 2B depicts a block diagram on de-enveloping on 4 received datastreams from 4 satellites with locally available digital envelopes andthen reconstituting the original sub-files via a 4-to-4 K-demuxingaccording to embodiments of this invention.

FIG. 2C depicts another block diagram on digital enveloping for 4K-muxed digital files by a sender at a source, sending 4 digitallyenveloped outputs to a destination via multiple satellites, according tosome embodiments of this invention.

FIG. 2D depicts another block diagram on de-enveloping on 4 receiveddata streams from 4 satellites with a locally available digital envelopeand then reconstituting the original sub-files via a 4-to-4 K-demuxingaccording to embodiments of this invention.

FIG. 2E depicts simulation results for enveloping/de-enveloping; amodified replicate of FIG. 5D from U.S. Pat. App. Pub. No. 20150032706A1.

FIG. 3 depicts a block diagram on “sealing” digital envelopes for anembedded digital file via a K-muxing processor by a sender at a source,sending all 4 outputs as the digitally enveloped data to a destinationvia multiple UAVs, and “de-enveloping” the digital envelopes andrecovering the embedded data at the destination in accordance toembodiments of this invention.

FIG. 3A depicts a block diagram on digital enveloping for 4 K-muxeddigital files by a sender at a source, sending 4 independent digitallyenveloped outputs to a destination via multiple UAVs, according to someembodiments of this invention.

FIG. 3B depicts a block diagram on de-enveloping on 4 received datastreams from 4 UAVs with locally available digital envelopes and thenreconstituting the original sub-files via a 4-to-4 K-demuxing accordingto embodiments of this invention.

FIG. 4 illustrates a block diagram on (1) K-muxing 3 digital files into4 K-muxed or K-transformed files, and then enveloping the K-muxed filesby a sender at a source, (2) enveloped data sets transported through 4different satellites to 3 destinations, and (3) in each destination adesignated signal is reconstituted through both de-enveloping thereceived signals and K-demuxing the recovered K-muxed digital data setsin accordance to embodiments of this invention.

FIG. 4A depicts a block diagram on K-muxing 3 data streams into 4K-muxed data streams and then digital enveloping 4 K-muxed digitalstreams by a sender at a source before sending the 4 digitally envelopedoutputs to a destination via multiple satellites, according to someembodiments of this invention.

FIG. 4B depicts a block diagram on de-enveloping on 4 received datastreams from 4 satellites with locally available digital envelopes andthen reconstituting the original sub-files via a 4-to-4 K-demuxingaccording to embodiments of this invention.

FIG. 4C illustrates a different configuration from FIG. 4A forenveloping 4 K-muxed information streams.

FIG. 4D illustrates a configuration complementary to the configurationin FIG. 4C for enveloping 4 K-muxed information streams.

FIG. 5 illustrates a block diagram on (1) K-muxing 3 digital files into4 K-muxed or K-transformed files, enveloping the K-muxed files, and thenmultiplexing the enveloped data streams via conventional FDM, TDM, CDMor combinations of all above by a sender at a source, (2) sending themultiplexed and enveloped data streams through 4 different transponders,time-slots, frequency slots, or CDM channels of a satellite to 3destinations, and (3) in each destination a designated signal isreconstituted through both de-enveloping the received signals andK-demuxing the recovered K-muxed digital data sets in accordance toembodiments of this invention.

FIG. 5A depicts a block diagram on K-muxing 3 data streams into 4K-muxed data streams, digital enveloping 4 K-muxed digital streams, andthen multiplexing them via conventional muxing techniques by a sender ata source before sending the 4 digitally enveloped outputs to adestination via a satellite, according to some embodiments of thisinvention.

FIG. 5B depicts a block diagram on (1) receiving and demuxing thereceived signals, (2) de-enveloping on 4 received data streams from 4channels from a satellite with locally available digital envelopes andthen (3) reconstituting the original sub-files via a 4-to-4 K-demuxingaccording to embodiments of this invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to distributed transport paths withbuilt-in redundancy via an M-to-M wavefront multiplexing (K-muxing)techniques, where M≥2 and must be an integer. The M inputs to theK-muxing comprising N streams of information data with additional M-Nknown data files, where N≥1 and is an integer. The M independent inputdata streams are transformed and concurrently converted into K-muxeddomain with M output wavefront components (wfcs). Only M′ of the Moutputs will be used for data transport and/or data storage on cloud,where M−N≤M′≤M, M′≥1 and is an integer.

Furthermore, any one of the known data files may be chosen to serve as adigital transporting envelope and will be processed accordingly in anenveloping process as a part of the M-to-M K-muxing.

Multiple inputs to an M-to-M K-muxing processor are properly“emphasized” or “weighted” so that at least one of the M outputs willbecome a “carrier” or a digital enveloped data stream for transportingembedded message. The selected “carrier” shall appear substantiallyidentical to the appearance of the selected digital envelope to humansensors. The identical appearance comprises unique and easilydistinguishable features from other digital data files. These featuresmay be visual pictures, videos, audio music, word files, or multimediafiles

At least one of the enveloped data streams will be sent to a destinationvia cloud. An enveloped data stream may appear as a digital picture, avideo clip, a music clip, an audio recording, or a digital cartoon whilebeing transported through wireless links. Just as functions of regularenvelopes, these digital envelopes may convey context and authors of theembedded mail, a preview of intentions and moods of the author, and/orinformation of where the embedded mail was originated.

The digital envelope and the enveloped digital data stream shall havesubstantially identical features which are identifiable anddistinguishable by human sensors; hearing, visually or both.

At destination, a desired receiver shall reconstitute the embeddedinformation data by a wavefront demultiplexing (K-demuxing) as the postprocessing while accessing the known file of the original digitalenvelope.

The present invention discloses operation concepts, methods andimplementations of enveloping/de-enveloping via wavefront multiplexingfor wireless transport as depicted in FIG. 1A. Similar techniques can beapplied to video streaming, secured data storage services, secured filetransfers, and other applications via wireless connectivity and/orInternet Clouds. The embodiments of present inventions comprise threeimportant segments including (1) the pre-processing for enclosing a mailin a selected envelope, i.e. the K-muxing, at a source; (2) transportingembedded mails via enveloped digital streams via wireless links and/orcloud, and (3) a post-processing of retrieval or de-enveloping, i.e. theK-demuxing, at a destination. We will depict both pre-processing and apost-processing as an example for illustrating the operation concepts.

In principle, the pre-processing and the post-processing are allperformed in user segments and performed in equipment at the user end.For satellite communications, these enveloping/de-enveloping may also beperformed in teleport facilities of an operator. The operator willaggregate the K-muxed data sets from distributed satellites covering acommon service area.

FIG. 1 is a modified replicate of FIG. 1 in US Patent ApplicationPublication No. US 2015/0032706 A1 and depicts an operationcommunications concept 110 between a sender at a source and a receiverat a destination. The modifications are on two indicators; “130” changedto “116” and “140” altered to “126”.

The sender takes advantages of a 2-to-2 K-muxing processor for sealingor enveloping 116 a set of input data S(t) by a selected digitalenvelope E5(t). The input data is an English phrase “Open Sesame” andits Chinese translation in a word format written in 4 Chinese charactersand associated pronunciation symbols. The chosen digital envelope is adigital picture of a famous painting of “a running horse” by a Chinesepainter, Xu Beihong, in early 1900's. There are 11 digital envelopes ina candidate envelope folder 180 commonly known to a user community whichboth the sender and the receiver belong to. There are two outputs fromthe K-muxer; one is for the enveloped mail Es(t), and the other Ed(t)(not indicated) which is grounded. The Es(t) is a result ofpixel-by-pixel processing from the two inputs data files; S(t) andE5(t). The K-muxing features a 2*2 Hadamard transform. S(t) and E5(t)will be “scaled” properly to enable Es(t) appearance substantiallyidentical to that in E5(t); as discussed in the US patent applicationpublication no. 2014/0081989A1 extensively. In this case, the runninghorse in Es(t) appears to be a flipped image of the same house in E5(t).

After the K-muxing, Es(t) is an enveloped data stream, and is the onlyfile to be sent to a destination via IP networks 010. Es(t) featureswith a visual appearance nearly identical to the picture of the famousrunning horse in E5(t).

At the destination, a receive shall reconstitute the embedded message of“Open Sesame” written in Chinese by de-enveloping as post-processing 140only when the digital picture of the original envelope is available tothe receiver. The post processing for de-enveloping 126 is implementedto perform the 2*2 K-demuxing transform, reconstituting the embeddedinformation data stream S(t). There is only one communication linksending and receiving Es(t) via cloud 010.

Embodiment 1

FIG. 1A, derived from FIG. 1 , depicts a concept of communications via atransponding satellite between a sender at a source 112 and a receiverat a destination 122. There are three segments including (1) apre-processor for enveloping 116 at a communications source or a source112, (2) a communications channel including a communicate satellite 030,and (3) a post processing for de-enveloping 126 at a communicationsdestination or a destination 122 downstream from the satellite 030. Theinformation data S(t) and the digital envelope E5(t) are identical tothose in FIG. 1 .

There is only one communications link for sending Es(t) from the source112 to the satellite 030 and one link from the satellite 030 to thedestination 122 sending transponded Es(t) or re-generated Es(t). Nosufficient information is transported at any time for un-intended usersin these two communications links to recover the embedded informationS(t).

Enveloping 116:

For enveloping 116 in a pre-processor in the communications source 112,a 2-to-2 K-muxing transform converts an input information data S(t) anda selected digital envelope stream E5(t) from a candidate envelopefolder 180 to two output data streams, i.e. Es(t), and Ed(t), where:Es(t)=S(t)+am*E5(t)  (1-1)Ed(t)=−S(t)+am*E5(t),  (1-2)

where am>>1 is a magnification factor, and image dependent, usually setbetween 5 and 30. Ed(t) is grounded. Effectively, a 2-to-2 Hadamardmatrix (HM) has been chosen for the transform of K-muxing. Equations(1-1) to (1-2) can be written in a matrix form as

$\begin{matrix}{O = {{HM}*I}} & (2) \\{{{where}\text{:}\mspace{14mu} O} = {\left\lbrack {{O\; 1},{O\; 2}} \right\rbrack^{T} = \left\lbrack {{{Es}(t)},{{Ed}(t)}} \right\rbrack^{T}}} & \left( {2\text{-}1} \right) \\{{HM} = \begin{bmatrix}1 & 1 \\{- 1} & 1\end{bmatrix}} & \left( {2\text{-}2} \right) \\{I = {\left\lbrack {{I\; 1},{I\; 2}} \right\rbrack^{T} = \left\lbrack {{S(t)},{{am}*E\; 5(t)}} \right\rbrack^{T}}} & \left( {2\text{-}3} \right)\end{matrix}$

The input ports of a K-muxing processor, or a K-muxer, are referred toas slices, and its output ports are wavefront components (wfc's). Thetwo input data sets S1 and am*E5, are connected to the input ports, i.e.slice 1, and slice 2 of the K-muxer respectively. The 2 output data setsi.e. O1-O2, are connected to the output ports, i.e. wfc1-wfc2, of theK-muxer in the pre-processing respectively.

In general, a 2-to-2 K-muxing processor features 2 orthogonal wavefrontvectors or WFV's. Let us define a coefficient wjk of a WF transformationto be the coefficient at the j^(th) row and k^(th) column of the K-muxer130. A WFV of the K-muxer in pre-processing 130 featuring a distributionamong the 2 outputs, i.e. O1-O2 at the 2 WF component ports wfc1-wfc2,is defined as a 2-dimensional vector. They are mutually orthogonal. Thetwo wavefront vectors (WFVs) of the K-muxer are:WFV1=[w11, w21]^(T)=[1, −1]^(T)  (3.1)WFV2=[w12, w22]^(T)=[1, 1]^(T)  (3.2)

S(t), and E5(t) are “attached” to the 2 WFVs by respectively connectedto the two input ports of the K-muxing device in the preprocessing. Allcomponents of the 2 orthogonal WFVs are related to input and output portnumbers or (spatial) sequences, but are independent from the input andoutput data sets.

The arithmetic operations of “linear combinations” may operate on blocksof information data after all inputs are aligned as digital informationstreams sample-after-sample for various inputs. A “byte” of data may be“selected” as a sample and a block of X samples, i.e. A sample of 7bytes of a digital data stream will be treated as a numerical number forcalculations in K-muxing transforms. Two streams of 7-byte samples maybe the respective inputs of the 2-to-2 WF muxer. A block size of samplesof 8 bytes in this case, will be reserved for the results of arithmeticoperations on a number of the digital streams to avoid issues ofoverflows and underflows at the two outputs of the K-muxing transforms.There shall be 12.5% in data size overhead of the 7 byte arithmeticoperations, with respect to the results in 8 byte forms in the outputs.In different embodiments, we may choose blocks with a block length of 99bytes for arithmetic operation, i.e. X=99, reducing the arithmeticoperation overhead to 1%.

The 7 byte arithmetic operations shall also feature 14.28% or 1/7 indata size overhead with respect to the 7 byte inputs.

There are other choices in selecting data blocks for arithmeticoperations of linear combinations or weighted sums in the K-muxingtransformations. For imaging processing, a pixel by pixel as operationblocks may be more important preserving unique features for someapplications, or a row or a column of pixels as a data block forefficient usage of transporting bandwidth.

In this example, only one (Es) of the two outputs (Es and Ed) is sent tothe destination 122. The intended receiver must have “additionalinformation” in order to reconstitute the embedded message or the mail;“Open Sesame” and its Chinese translation in a word format written in 4Chinese Characters. The additional information is the original file ofthe selected digital envelope E5(t).

In general, at least one of K-muxed output streams from higher ordermuxing or multilayer enveloping will be sent to the communicationdestination 122 via satellites 030. The embedded mail is in theenveloped digital data stream. The higher order muxing is usuallyreferred to an N-to-N K-muxing with N in between 4 and 5000. The numbersof K-muxed streams to be sent to a destination shall be always smallerthan a critical numbers of muxed data streams; Ncr.

For un-intended receivers, there are not enough information in the NcrK-muxed data streams flowing through the satellite links to reconstitutethe embedded information. Additional information known a priori isrequired for reconstituting enveloped (embedded) original data.

On the other hand, in a different embodiment where both outputs (Es andED) were delivered to a receiver, both the embedded mail S(t) and theselected original digital envelope E5 could all be reconstitutedindependently at the destination 122 without any additional a prioriknown information.

Communication Satellite 030:

Referring to FIG. 1A again, only one K-muxed file is sent from thesource 112 to the destination 122 via the satellite 030. The originaldigital envelope file is known a priori to both the sender at a source112 and receiver at the destination 122. Therefore, the required channelbandwidth for Es(t) is about the same as that of the embedded message,S(t). The differentials in required bandwidths between that for Es(t)and that for S(t) are due to a pre-processing overhead.

De-Enveloping 126:

De-enveloping 126 in a post processor for data retrieval comprises aK-demuxing transform, converting the received K-muxed data into anoutput of embedded data file S(t). The original digital envelope file,E5(t), is also used as one input to the K-demuxing transform in thede-enveloping 126. The received K-muxed data is substantially equivalentto the corresponding output data set, Es(t), of the enveloping 116 inthe source 110, if not contaminated, and is therefore represented byEs(t) or Es′(t). Similarly, the recovered embedded data file issubstantially equivalent to the input data sets, S(t), and is thereforereferred to as S(t) or S′(t).

According to equation (1-1); the recovered embedded data can be derivedfrom the received K-muxed data Es(t) and the known digital envelopeE5(t)S(t)=Es(t)−am*E5(t)  (4)where the factor “am” can be experimentally optimized or through apriori knowledge set. Therefore, the missing second output of theK-muxing can also be re-constructed in the destination according toEquation (1-2) and Equation (4)Ed(t)=−Es(t)+2*am*E5(t),  (5)

A 2-to-2 Hadamard matrix with scaling factor of ½ may be chosen as the2-to-2 K-demuxer. The matrix elements of 2-to-2 Hadamard matrix feature“1” or “−1” only. The relationship may be written in a matrix form asSM=HM*D  (6)where: D=[D1, D2]^(T)=[Es(t), Ed(t)]^(T)  (6-1)SM=[S(t), am E5(t)]^(T)  (6-2)

-   -   HM is a 2-to-2 Hadamard matrix in equation (2-2).

The input ports of a K-demuxing transform in de-enveloping 126 arereferred to as wavefront components (wfcs), i.e. wfc1, and wfc2, and itsoutput ports are slices, i.e. slice1, and slice2. In this example, the 2input data sets, i.e. Es(t) and Ed(t), are connected to its input portswfc1-wfc2 of the K-demuxing transform in the de-enveloping 140,respectively. The retrieved data set, S1, is from its first outputports. Normally the second output of the de-enveloping 126 will be“grounded” for most applications with customized receivers.

Other Embodiments Via FIG. 1A

In a different embodiment, the first output Es(t) from the enveloping116 in the pre-processor at the source 112 as depicted is sent to thesatellite 030, while the respective second output Ed(t) is no longergrounded but sent aperiodically via a second channel in the samesatellite 030, through a second satellite (not shown), or a differentchannel such as cloud, to the destination 122 to reconstitute a copy ofthe original digital envelope at the destination 122. Based on Equations(1-1) and (1-2),S(t)=(Es(t)+Ed(t))/2  (7-1)E5(t)=(Es(t)−Ed(t))/(2*am)  (7-2)The reconstructed digital envelope, E5(t), may be utilized forcomparison with the known on-filed digital envelope for the integrity ofreceived data S(t). It is a good indication that the received embeddeddata has been compromised only if a set of comparison results showingthe two digital envelopes are different.

In another embodiment, the respective second output Ed(t) from theenveloping 130 at the source is sent concurrently and continuously via asecond channel in the same satellite 030 or through a different channelsuch as cloud, to reconstitute the embedded message S(t) and a copy ofthe original digital envelope E5(t) at the destination 122 according toequations (7-1) and (7-2). The reconstructed digital envelope, E5(t),will be stored on file for receiving embedded data in future. It is agood technique to deliver digital envelopes to receivers indestinations.

Furthermore, when S(t) is another selected envelope, say E4(t), at thesource 110, the transmissions of Es(t) and Ed(t) of equation (1-1) and(1-2) via two separate and independent channels shall providetransporting privacy of E4(t) from the source 112 to the destination122. These two independent channels may even be in two differenttransponders of the same depicted satellite 030.

Embodiment 2

FIG. 2 depicts a concept of communications via multiple transpondingsatellites between a sender at a source 112 and a receiver at adestination 122. There are three segments including (1) a pre-processingat a communications source or a source 112, (2) a communicationsconnectivity including multiple communication satellites 030-1 to 030-4,and (3) a post processing at a communications destination or adestination 122 downstream from the satellites 030-1 to 030-4. Theinformation data Sx(t) is for user x and digital envelopes are selectedfrom a candidate envelope folder 180 which comprising of commonly knowndigital envelopes to both the source 112 and the destination 122. Thereare probing signals, Pbx, will be incorporated as input at the source112 and recovered at the outputs for continuously monitoring the“health” of the dynamic communications connectivity.

In the depicted example, there are 4 K-muxed outputs ye1, ye2, ye3, andye4 from a transform of enveloping 130 in the source 112. Afterfrequency up-converted, modulated, and power amplified, the firstinformation stream ye1 is sent to a first satellite 030-1. Similarly,the second information stream ye2, the third information stream ye3, andthe fourth information stream ye4 are respectively transported via thesecond satellite 030-2, the third satellite 030-3, and the fourthsatellite 030-4 to the destination 122. The RF frequencies, modulations,power levels for the 4 outputs ye1, ye2, ye3, and ye4 linking to the 4satellites 030-1 to 030-4 may be different completely. At thedestination 122 after low-noise, demuxing transformed may be implementedfor both (1) de-enveloping received information data substreams and (2)de-aggregating the de-enveloped information substreams to reconstituteoriginal information data stream Sx(t) for user x and the probing datastream Pbx.

The 4 satellites may be transponding satellites which may be in a samefrequency slot or in different frequency bands at different orbitalslots, regenerative satellites with on-board de-modulators andre-modulators, or combinations of all above. The propagation delaysshall be equalized to line-up the data frames of information datastreams. For 10 Mbps streams the timing accuracy may be in the order of100 nanoseconds or 10⁻⁷ seconds.

In comparing with time synchronization requirements on applications ofcoherent WF muxing among multiple Ku band channels with carriers at ˜12GHz band, the timing accuracy must be better than 10⁻¹³ seconds forlining up carrier phases within 1°.

The block diagrams in FIG. 2A and FIG. 2B are complementary to eachother. FIG. 2A illustrates more detailed functional blocks at the source112 in FIG. 2 . There are three major and separate functional blocks;the functions of segmenting 114, K-muxing 130, and enveloping 116-1 to116-4. The enveloping 116-1 to 116-4 are concurrently carried out by 4sets of 2-to-2 K-muxing with functions identical to the preprocessing130 in FIG. 1A. There are two sets of sequential K-muxing operations inFIG. 2A; the K-muxing 130 for generating 4 different aggregations[y1,y2,y3,y4] from 4 inputs [Pbx, xa, xb, xc], each aggregation followedby one of the 4 enveloping processors 116-1 to 116-4, each of whichperforms a 2-to-2 K-muxing transform under customized configurations.

The first inputs a probing data stream, Pbx. An information data streamSx(t), intended for a user x in a destination, is segmented into 3information data substreams xa, xb and xc which are connected to 3 ofthe 4 inputs of the K-muxing 130.

There are 4 outputs from the K.-muxing function 130; y1, y2, y3, and y4;which shall be referred to as 4 K-muxed data substreams are thendigitally enveloped by the 4 enveloping processor 116-1 to 116-4. Theenveloped K-muxed data substreams, ye1 to ye4, are then sent to the 4satellites 030-1 to 030-4 concurrently after properly and independentlymodulated, frequency converted, filtered, and then power amplified.

The K-muxing 130 is characterized by the following 4 simultaneous linearequations;W11*Pbx+W12*xa+W13*xb+W14*xc=y1  (8-1)W21*Pbx+W22*xa+W23*xb+W24*xc=y2  (8-2)W31*Pbx+x′32*xa+x′33*xb+W34*xc=y3  (8-3)W41*Pbx+W42*xa+W43*xb+W44*xc=y4  (8-4)These equations can be written in matrix form;[W][X]=[Y]  (8)where[X]=[Pbx, xa, xb, xc]^(T)  (8a)[Y]=[y1, y2, y3, y4]^(T)  (8b)[W]=[Wij in a 4×4 format]  (8c)

When [W] is a 4×4 Hadamard matrix or any matrix with an existing inversematrix, the 4 linear equations (8-1) to (8-4) are independent. When [Y]is known and/or available at a destination 122, all 4 unknown componentsin the [X], or Pbx, xa, xb, and xc can be solved or calculated.

It is noticed that for any scenarios where the Pbx is known at adestination, the 4 simultaneous linear equations (8) can be written asW12*xa+W1.3*xb+W14*xc=y1−W11*Pbx  (9-1)W22*xa+W23*xb+W24*xc=y2−W21*Pbx  (9-2)W32*xa+W33*xb+W34*xc=y3−W31*Pbx  (9-3)W42*xa+W43*xb+W44*xc=y4−W41*Pbx  (9-4)

When [Y] is available from satellites and Pbx is known a priori, thereare 4 simultaneous linear equations for all 3 unknown components in the[X]; or xa, xb, and xc. Therefore there is one built-in redundancy inthe four components of [Y]. We only need three of the 4 equations (9-1)to (9-4) solving for the three unknowns; xa, xb, and xc.

In the 4 enveloping processors 116-1 to 116-4, each featuring 2 inputsand two outputs shall perform the identical enveloping transform asthose shown in the pre-processor (enveloping) 130 with two inputs andtwo outputs in FIG. 1A. In anyone of the 4 enveloping processors 116-1to 116-4, one of the two inputs is a K-muxed segmented data sub stream(one of y1 to y4) and the other input is a selected digital envelopestream from a candidate envelope folder 180. The selected envelopes aree1, e2, e3, and e4 for the enveloping processors 116-1, 116-2, 116-3 and116-4, respectively. Furthermore only one of the two outputs is sent fora satellite relay and the other is grounded.

These digital envelopes (e1, e2, e3, and e4) are from a candidateenvelope folder 180. All the potential envelopes are stored in theenvelope folders, and shall be are known to both the source 112 and thedestination 122. We may choose 4 completely different digital envelopesfor all 4 K-muxed information data substreams; y1, y2, y3, and y4. Onthe other hand on the other extreme, we may select an identical envelopefor all 4 of them for transport to individual satellites 030-1 to 030-4.Mostly we choose some identical and other different envelopes.

The K-muxing 130 may be via orthogonal matrices or non-orthogonalmatrices, as long as their inverse matrices exist.

FIG. 2B illustrates more detailed functional blocks at the destination122 in FIG. 2 . It is also a corresponding block diagram of dataprocessing functions to those depicted in FIG. 2A. There are three majorand separate functional blocks; the functions of de-enveloping 126-1 to126-4, K-demuxing 140, and de-segmenting 124.

The enveloped K-muxed data substreams, ye1 to ye4, are recover from the4 satellites 030-1 to 030-4 after low-noise amplified, frequencyconverted, properly filtered, and then de-modulated.

In the 4 de-enveloping processors 126-1 to 126-4, each featuring 2inputs and two outputs shall perform the identical de-envelopingtransform as those shown in the post-processor (de-enveloping) 140 withtwo inputs and two outputs in FIG. 1A. In anyone of the 4 de-envelopingprocessors 126-1 to 126-4, one of the two inputs is a recoveredenveloped K-muxed segmented data substream (one of ye1 to ye4) and theother input is a selected digital envelope stream from a local digitalenvelope folder 180. Furthermore only one of the two outputs is sent forK-demuxing 140 and the other is grounded.

The 4 inputs to the K-demuxing 140; y1, y2, y3, and y4; referred to as 4recovered K-muxed data substreams which have been digitally de-envelopedby the 4 de-enveloping processor 126-1 to 126-4. These digital envelopesare from an envelope folder 180. All the potential envelopes are in theenvelope folders, and shall be are known to both the source 112 and thedestination 122.

The K-demuxing 140 must perform a corresponding transform which is aninverse transform to that of the K-muxing 130 in FIG. 2A, featuring anorthogonal matrix or a non-orthogonal matrix, as long as their inversematrices exist.

The 4 outputs from the K-demuxing 140 shall be the recovered Pbx datastream and 3 recovered segmented information data substreams xa, xb andxc The information data stream Sx(t), intended for a user x in thedestination 122, is reconstituted through the de-segmenting 124 from therecovered 3 information data substreams.

In scenarios with known Pbx at a destination 122, the receiver at thedestination 122 is required to capture any 3 of the 4 satellite-relayedor satellite-transponded enveloped K-muxed information substreams; ye1,ye2, ye3, ye3, and ye4. Three of the 4 de-enveloping processors 126-1 to126-4 shall de-envelope all three of them, recovering a set of three ofthe 4 K-muxed information data substreams; y1, y2, y3, and y4. Accordingto Equations (9-1) to (9-4), the K-demuxing 140 shall also be configuredfor solving three unknowns (xa, xb, and xc) based on only threerecovered K-muxed information substreams; a set of three from [y1, y2,y3, y4].

The block diagrams in FIG. 2C and FIG. 2D are complementary to eachother in a configuration for enveloping 4 K-muxed information substreamsby same formatted envelopes. FIG. 2C illustrates the configuration ofmore detailed functional blocks at the source 112 in FIG. 2 . There aretwo major and separate functional blocks; the functions of segmenting114, and those of K-muxing 130 which features concurrent enveloping. Aninformation data stream Sx(t), intended for a user x in a destination,is segmented into 3 information data substreams xa, xb and xc which areconnected to 3 of the 4 inputs of the K-muxing 130. The 4^(th) input isa data stream of a digital envelope Ex selected from the candidateenvelope folder 180.

Let us assume a 4-to-4 Hadamard transform be the matrix for K-muxing130. The K-muxed files ye1, ye2, ye3 and ye4 are the 4 outputs from theK-muxing 130. To create camouflaged effects on the 4 K-muxed data forwireless transport, the original digital envelope Ex has been “heavilyweighted” before the K-muxing 130 operation.

As an example, E5 features a Chinese painting of a “running horse” shownin FIG. 1 , and E5(t) is selected as Ex for the input of y1 in a digitalpicture format. In order to assure that the E5(t) image of the Chinesehorse painting in y1 to be more dominant features in the 4 multiplexedoutputs as camouflaged, we have emphasized the pixel intensities of y1via:

$\begin{matrix}{\begin{bmatrix}{{ye}\; 1} \\{{ye}\; 2} \\{{ye}\; 3} \\{{ye}\; 4}\end{bmatrix} = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} \\{+ 1} & {- 1} & {- 1} & {+ 1}\end{bmatrix}\begin{bmatrix}{{am}*y\;\underset{\_}{1}} \\{y\; 2} \\{y\; 3} \\{y\; 4}\end{bmatrix}}} & (10)\end{matrix}$where am>1. Usually the amplification factor “am” is set to be greaterthan 10. It is also assumed the 4 inputs which were re-formatted into apixel lattice have been fully equalized. Depending on the selection of acamouflaging image, the emphasizing factor, am, may applied to any ofthe input images in [Y]. As a result, the image of “running horse”painted by Xu Baihong becomes dominant among the 4 participating inputsand appears on all 4 outputs of the K-muxing 130. The 4 K-muxed data,i.e. ye1, ye1, ye3 and ye4, shall feature a same appearance of “runninghorse” with various intensity settings; as depicted in the 4 digitalimages on the second row of FIG. 2E. We shall describe FIG. 2E infollowing paragraphs in details.

FIG. 2D illustrates more detailed functional blocks at the destination122 in FIG. 2 . It is also a corresponding block diagram of dataprocessing functions to those depicted in FIG. 2C. There are two majorand separate functional blocks; the functions of K-demuxing 140including de-enveloping, and de-segmenting 124.

The 4 inputs to the K-demuxing 140; ye1, ye2, ye3, and ye4; will bedigitally de-enveloped and de-aggregated concurrently. The K-demuxing140 shall perform an inverse transform to a corresponding one inK-muxing 130 in FIG. 2C. Its transform is characterized by:

$\begin{matrix}{\begin{bmatrix}{{am}*y\; 1} \\{y\; 2} \\{y\; 3} \\{y\; 4}\end{bmatrix} = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} \\{+ 1} & {- 1} & {- 1} & {+ 1}\end{bmatrix}\begin{bmatrix}{{ye}\; 1} \\{{ye}\; 2} \\{{ye}\; 3} \\{{ye}\; 4}\end{bmatrix}}} & (11)\end{matrix}$

where [y1, y2, y3, y4]=[E5, xa, xb, xc].

Four outputs from the K-demuxing 140 shall include a recovered digitalenvelope E5, and 3 recovered segmented information data substreams xa,xb, and xc. The information data stream Sx(t), intended for user x inthe destination 122, is reconstituted through the de-segmenting 124 fromthe recovered information data substreams [xa, xb, xc].

An original digital envelope from a candidate envelope folder 180 shallbe used for a digital comparison 182 to the recovered envelopebit-by-bit for data integrity monitoring.

FIG. 2E is a modified replicate of FIG. 5 in US patent applicationpublication No. 20150032706. There are 12 images on three panels. Thelabels have been modified to become consistent with those in this patentapplication. The four digital streams depicted on the top panel 521 arethe 4 inputs to equation (10); y2, y3, y4, and y1 where y2=xa, y3=xb,y4=xc, and y1=E5. The 4 outputs of Equation (10) depicted on the middlepanel 522 are [ye1, ye2, ye3, ye4]. As shown on their appearances, eachof the 4 outputs has been digital enveloped by a common envelope E5 butwith various brightness.

The 4 images on the bottom panel 523 are result of K-demuxing 140characterized by Equation (11). The four inputs to Equation (10) are thedigital streams on the middle panel 522, and corresponding 4 concurrentoutputs are the digital image streams [y1, y2, y3, y4], which equal to[xa, xb, xc, E5] on the bottom panel 523.

In a different embodiment, referring back to FIG. 2 , only 3 of the 4outputs [ye1, ye2, ye3, ye4] from a source 112 are delivered to three ofthe 4 satellites 030-1 to 030-4. In this embodiment with a configurationof FIG. 2A and FIG. 2B, the receiver in a destination 122 must haveaccess of the probing data stream Pbx in order to recover [xa, xb, xc]through K-demuxing 122 and then reconstituting Sx(t) from [xa, xb, xc]via a de-segmenting function 124.

Similarly, with a configuration of FIG. 2C and FIG. 2D, the receiver ina destination 122 must have access of the digital envelope data streamEx in order to recover [xa, xb, xc] through K-demuxing 140 and thenreconstituting Sx(t) from [a, xb, xc] via a de-segmenting function 124.

In other embodiments of FIG. 2 , FIG. 2A, FIG. 2B, FIG. 2C and FIG. 2D,any satellite links between a source and a destination may be replacedby airborne platform based links, a cellular links, wireless terrestriallinks, and/or links via cloud.

Embodiment 3

FIG. 3 depicts a communications concept via multiple airborne platforms020-1 to 020-4 including unmanned air vehicles (UAVs) between a senderat a source 112 and a receiver at a destination 122. There are threesegments including (1) a pre-processing at a communications source or asource 112, (2) a communications connectivity including multiple linksvia airborne platforms 020-1 to 020-4, and (3) a post-processing at acommunications destination or a destination 122 downstream from theairborne platforms or air-platforms 020-1 to 020-4. The information dataSx(t) is for user x and digital envelopes are selected from a candidateenvelope folder 180 which comprising of commonly known digital envelopesto both the source 112 and the destination 122. There are probingsignals, Pbx, which will be incorporated as an input at the source 112and recovered at the outputs for continuously monitoring the “health” ofthe dynamic communications channels in the destination 122. Thisconfigurations are identical to the ones in FIG. 2 , except thesatellites 030-1 to 030-4 in FIG. 3 are replaced by the airborneplatforms 020-1 to 020-4. Furthermore in FIG. 3 , modulators 018-1 to018-4, and de-modulators 022-1 to 022-4 are high-lighted; indicatingthat the incoherent K-muxing/K-demuxing are applied to information datastreams not on signal data (waveform) streams.

In the depicted example, there are 4 K-muxed outputs ye1, ye2, ye3, andye4 from the source 110. After a modulations 018-1 followed by frequencyup-conversion, and power amplification, the first information stream ye1is sent to a first air-platform 020-1. Similarly, the second informationstream ye2 after a modulation 018-2, the third information stream ye3after a modulation 018-3, and the fourth information stream ye4 after amodulation 018-4 are respectively transported via the secondair-platform 020-2, the third air-platform 020-3, and the fourthair-platform 020-4 to the destination 122. At the destination 122, 4received signals from the air-platforms 020-1 to 020-4 after low-noiseamplification, filtering, frequency-conversion, will be converted bybase-band de-modulation 022-1 to 022-4 into 4 enveloped K-muxedinformation data substreams. K-demuxing transforms are implemented forboth de-enveloping received information data substreams, andde-aggregating the de-enveloped information substreams reconstitutingoriginal information data stream Sx(t) for user x and the probing datastream Pbx.

The 4 air-platforms 020-1 to 020-4 may feature transponding repeatersoperated in different frequency bands at different orbiting/parking orcruising slots, regenerative repeaters with on-board de-modulators andre-modulators, or combinations of both. The propagation delays shall beequalized to lineup the data frames of information data streams. For 10Mbps streams the timing accuracy shall be in the order of 100nanoseconds or 10⁻⁷ seconds.

The block diagrams in FIG. 3A and FIG. 3B are complementary to eachother. FIG. 3A illustrates more detailed functional blocks at the source112 in FIG. 3 . There are three major and separate functional blocks;the functions of segmenting 114, K-muxing 130, and enveloping 116-1 to116-4. The enveloping 116-1 to 116-4 are concurrently carried out by 4sets of 2-to-2 K-muxing with functions identical to the enveloping 116in FIG. 1A.

There are two sequential K-muxing operations for data aggregating anddata enveloping in FIG. 3A. The K-muxing 130 generates 4 aggregations[y1, y2, y3, y4] from the same inputs [Pbx, xa, xb, xc]. The first inputof the K-muxing 130 is a probing data stream, Pbx. An information datastream Sx(t) at a source 110, intended for a user x in a destination122, is segmented into 3 information data substreams xa, xb, and xcwhich are connected to the remaining 3 of the 4 inputs of the K-muxing130.

There are 4 outputs from the K-muxing function 130; y1, y2, y3, and y4;which shall be referred to as 4 K-muxed data substreams are thendigitally enveloped by the 4 enveloping processor 116-1 to 116-4. The 4enveloping processors 116-1 to 116-4 performing individually a 2-to-2K-muxing transform under customized configurations featuring two outputseach and one of two is grounded.

The enveloped K-muxed data substreams, ye1 to ye4, are properlymodulated by modulators 018-1 to 018-4 before being sent to the 4air-platforms 020-1 to 020-4 concurrently after frequency converted,filtered, and then power amplified.

The 4-to-4 K-muxing 130 for data aggregation is characterized by the 4simultaneous linear equations (8-1) to (8-4). It may be implemented as atransform by a 4×4 Hadamard matrix or any matrix with an existinginverse matrix. As a result, the 4 linear equations (8-1) to (8-4) areindependent. When [Y] or [ye1, ye2, ye3, ye4] becomes known and/oravailable at a destination 122, all 4 unknown components in the [X], or[Pbx, xa, xb, xc] can be solved or calculated.

It is noticed that for any scenarios where the Pbx is known at adestination, the 4 simultaneous linear equations (8) can be written asequations (9-1) to (9-4). When [Y] is available from air-platforms andPbx is known a priori, there are 4 simultaneous linear equations for all3 unknown components in the [X]; or xa, xb, and xc. Therefore there is abuilt-in redundancy in the four components of [Y]. We only need anythree of the 4 equations (9-1) to (9-4) in solving for the threeunknowns; xa, xb, and xc.

In the 4 enveloping processors 116-1 to 116-4, each featuring 2 inputsand two outputs shall perform the identical enveloping transform asthose shown in the enveloping 116 with two inputs and two outputs inFIG. 1A. In anyone of the 4 enveloping processors 116-1 to 116-4, one ofthe two inputs is a K-muxed segmented data substream (one of y1 to y4)and the other input is a selected digital envelope stream from acandidate envelope folder 180. The selected envelopes are e1, e2, e3,and e4 for the enveloping processors 116-1, 116-2, 116-3 and 116-4,respectively. Furthermore only one of the two outputs is sent for acorresponding air-platform and the other is grounded. We may choose 4completely different digital envelopes for all for 4 K-muxed informationdata substreams; y1, y2, y3, and y4. On the other hand, we may select anidentical envelope for all 4 of them for transport to individualair-platforms 020-1 to 020-4.

FIG. 3B illustrates more detailed functional blocks at the destination122 in FIG. 3 . It is also a corresponding block diagram of dataprocessing functions to those depicted in FIG. 3A. There are three majorand separate functional blocks; the functions of de-enveloping 126-1 to126-4, K-demuxing 140, and de-segmenting 124.

The enveloped K-muxed data substreams, ye1 to ye4, are recovered fromthe 4 air-platforms 020-1 to 020-4 after low-noise amplified, frequencyconverted, properly filtered, and then de-modulated by demodulators022-1 to 022-4.

In the 4 de-enveloping processors 126-1 to 126-4, each featuring 2inputs and two outputs shall perform the identical de-envelopingtransform as those shown in the de-enveloping 126 with two inputs andtwo outputs in FIG. 1A. In anyone of the 4 de-enveloping processors126-1 to 126-4, one of the two inputs is a recovered enveloped K-muxeddata substream (one of ye1 to ye4) and the other input is a selecteddigital envelope stream from a local candidate envelope folder 180.Furthermore only one of the two outputs is sent for K-demuxing 140 andthe other is grounded.

The 4 inputs to the K-demuxing 140; y1, y2, y3, and y4; referred to as 4recovered K-muxed data substreams which have been digitally de-envelopedby the 4 de-enveloping processor 126-1 to 126-4. These digital envelopesare from an envelope folder 180. All the potential envelopes are in theenvelope folder, and shall be are known to both the source 112 and thedestination 122.

The 4 outputs from the K-demuxing 140 shall be the recovered Pbx datastream and 3 recovered information data substreams xa, xb and xc. Theinformation data stream Sx(t) intended for a user x in the destination122 is reconstituted through the de-segmenting 124 from the recovered 3information data substreams.

In another embodiment of FIG. 3 , FIG. 3A, and FIG. 3B, any air-platformlinks between a source and a destination may be replaced by satellitelinks, cellular links, wireless terrestrial links, and/or links viacloud.

In other embodiments with a known Pbx at the destination 122, thereceiver at the destination 122 is required to capture any 3 of the 4relayed or transponded enveloped K-muxed information substreams; ye1,ye2, ye3, ye3, and ye4 from 4 air platforms 020-1 to 020-1. Three of the4 de-enveloping processors 126-1 to 126-4 shall de-envelope all three ofthem, recovering a set of three of the 4 K-muxed information datasubstreams; y1, y2, y3, and y4. According to Equations (9-1) to (9-4),the K-demuxing 140 shall also be configured for solving three unknowns(xa, xb, and xc) based on only three recovered K-muxed informationsubstreams; a set of three from [y1, y2, y3, y4].

The cascaded K-muxing/demuxing configurations for separate dataaggregating and enveloping in FIGS. 3A and 3B can be modified similar tothose in FIG. 2C and FIG. 2D.

Embodiment 4

FIG. 4 depicts a block diagram of digital enveloping modified from thatof FIG. 2 . There are three user information data streams, Sx, Sy, andSz in a source 112 to be delivered to three individual users, x, y, andz at three different destinations 122 with (1) improved privacy viadigital enveloping and (2) enhanced availability via redundancy throughK-muxing over multiple information data streams. The source 112 and thedestinations 122 are under coverages of all 4 relaying satellites 030-1to 030-4.

The block diagram in FIG. 4 shows a concept of communications viamultiple satellites for concurrently delivering three information datastreams [Sx, Sy, Sz] from a sender at a source 112 to receivers atvarious destinations 122. There are three segments including (1) apre-processing at a communications source or a source 112, (2) amulti-link communications connectivity including multiple communicationsatellites 030-1 to 030-4, and (3) a post-processing at destinations 122downstream from the communications satellites 030-1 to 030-4. Theinformation data sets Sx(t), Sy(t), and Sz(t) are, respectively, forusers x, y, and z. Respective digital envelopes are selected from acandidate envelope file 180 in which digital envelopes known a priori toa user community are stored. Both a sender in the source 112 andreceivers at various destinations 122 are parts of the user community.There is a probing data stream, PBx, which will be incorporated as aninput at the source 112 and recovered at various destinations 122 forcontinuously monitoring the “health” of the communications connectivityfeaturing dynamic multiple-links. The connectivity in this example shallsurvive under a sufficient condition even when only 3 of the 4 links areavailable.

Preprocessing at the source 112 produces 4 enveloped K-muxed outputsye1, ye2, ye3, and ye4, as depicted in FIG. 4 . After frequencyup-conversion, modulation, proper filtering, and power amplification,the first information stream ye1 is sent to various destinations 122 viaa first satellite 030-1. Similarly, the second information stream ye2,the third information stream ye3, and the fourth information stream ye4are respectively transported to the designated destinations 122 via thesecond satellite 030-2, the third satellite 030-3, and the fourthsatellite 030-4.

At a first of the 3 destinations 122 after low-noise amplification,filtering, frequency-conversion, and de-modulation, both de-envelopingand de-aggregating are implemented in a post-processor via K-demuxing toreconstitute original information data stream Sx(t) for user x and theprobing data stream Pbx. The de-enveloping is to process 4 receivedenveloped information data streams from ye1, yre2, ye3, and ye4,removing the digital envelopes. The de-aggregating performs a customizedlinear combination on the 4 de-enveloped information streams restoring adesired user information data stream, Sx(t).

Similarly, at either a second or a third of the 3 destinations 122, apost-processor will reconstitute the probing data stream Pbx and anoriginal information data stream Sy(t) or Sz(t), respectively.

The 4 satellites may be (1) transponding satellites operated in a commonfrequency slot or different frequency bands at different orbital slots,(2) regenerative satellites with on-board de-modulators andre-modulators, or (3) combinations of both above. The transponders fromthe 4 satellites 030-1 to 030-4 may refer to 4 different transponders ina same physical satellite, or N transponders in a first satellite and(4−N) others in a second satellite, where N is 1, 2, or 3. It may alsobe other combinations from three satellites.

The propagation delays shall be equalized to lineup the data frames ofinformation data streams. For 10 Mbps streams, the timing accuracy shallbe in the order of 100 nanoseconds or 10⁻⁷ seconds.

The block diagrams in FIG. 4A and FIG. 4B are complementary to eachother. FIG. 4A illustrates more detailed functional blocks at the source112 in FIG. 4 . There are two major and separate functional blocks: thefunctions of information data stream mixing among 4 inputs via a 4-to-4K-muxing 130, and those of enveloping 116-1 to 116-4. The enveloping116-1 to 116-4 are concurrently carried out by 4 sets of 2-to-2 K-muxerswith functions identical to the enveloping 116 in FIG. 1A.

There are two sequential K-muxing operations in FIG. 4A. The K-muxing130 generating 4 aggregated outputs [y1, y2, y3, y4] among fourinformation data streams, each followed by one of the 4 envelopingprocessors 116-1 to 116-4.

The first input for the K-muxing 130 is a probing data stream, Pbx.Information data streams Sx(t), Sy(t) and Sz(t) intended for a user x ina first, a user y in a second, and a user z in a third of the 3destinations 122 are connected to last 3 of the 4 inputs of the K-muxing130, respectively. Four outputs of different aggregations by theK-muxing 130 are the 4 linear combinations among the inputs of fourinformation data streams, Pbx, Sx, Sy, and Sz. The 4 outputs from thefunction of K-muxing 130; y1, y2, y3, and y4; shall be referred to as 4K-muxed data streams.

The 4 outputs are then digitally enveloped by the 4 enveloping processor116-1 to 116-4; each performs a 2-to-2 K-muxing transform 116 undercustomized configurations. The enveloped K-muxed data streams, ye1 toye4, are then sent to the 4 satellites 030-1 to 030-4 concurrently afterproperly modulated, frequency converted, filtered, and then poweramplified.

We may set Sx(t)=xa, Sy(t)=xb, and Sz(t)=xz, and then the K-muxing 130is characterized by the identical 4 simultaneous linear equations (8-1)to (8-4). These equations can be written in a matrix form in equation(8). When [W] is a 4×4 Hadamard matrix or any matrix with an existinginverse matrix, the 4 linear equations (8-1) to (8-4) are independent.When [Y] is known and/or available at a destination 122, all 4 unknowncomponents in the [X], or [Pbx, xa, xb, xc] can be solved or calculated.

It is noticed that for any scenarios where the Pbx is known at adestination, the 4 simultaneous linear equations (8) can be written asequation (9-1) to (9-4). When [Y] becomes available from satellite linksand Pbx is known a priori, there are 4 simultaneous linear equations forall 3 unknown components in the [X]; or xa, xb, and xc. Therefore, thereis one built-in redundancy in the four components of [Y]. We only needthree of the 4 components in [Y] to solve for the three unknowns xa, xb,and xc via equations (9-1) to (9-4).

In the 4 enveloping processors 116-1 to 116-4, each featuring 2 inputsand two outputs shall perform the identical enveloping transform asthose shown in the function of enveloping 116 with two inputs and twooutputs in FIG. 1A. In any one of the 4 enveloping processors 116-1 to116-4, one of the two inputs is a K-muxed segmented data stream (one ofy1 to y4) and the other input is a selected digital envelope stream froma candidate envelope folder 180. The selected envelopes are e1, e2, e3,and e4 for the enveloping processors 116-1, 114-2, 116-3 and 116-4,respectively. Furthermore, only one of its two outputs is sent for asatellite communication channel and the other is grounded.

These digital envelopes (e1, e2, e3, and e4) are selected from acandidate envelope folder 180. All the digital envelopes in thecandidate envelope folder 180 shall be known to both the source 112 andthe destination 122. We may choose 4 completely different digitalenvelopes for all 4 K-muxed information data streams; y1, y2, y3, andy4. On the other hand, we may select an identical envelope fortransporting all 4 to individual satellites 030-1 to 030-4.

The K-muxing 130 may be via orthogonal matrices or throughnon-orthogonal matrices, as long as their inverse matrices exist.

FIG. 4B illustrates more detailed functional blocks at one of the 3destinations 122 in FIG. 4 . It is also a corresponding block diagram ofdata processing functions to those depicted in FIG. 4A. There are twomajor and separate functional blocks; the functions of de-enveloping126-1 to 126-4, and de-aggregating via K-demuxing 140.

The 4 enveloped K-muxed data streams, ye1 to ye4, are recovered from the4 satellites 030-1 to 030-4 after being low-noise amplified, frequencyconverted, properly filtered, and then de-modulated.

In the 4 de-enveloping processors 126-1 to 126-4, each featuring twoinputs and two outputs shall perform the identical de-envelopingtransform as those shown in the post-processor (de-enveloping) 126 inFIG. 1A. In any one of the 4 de-enveloping processors 126-1 to 126-4,one of the two inputs is a recovered enveloped K-muxed data stream (oneof ye1 to ye4) and the other input is a selected digital envelope streamfrom a local digital envelope folder 180. Furthermore, only one of thetwo outputs is sent for de-aggregating via K-demuxing 140 and the otheris grounded.

The 4 inputs to the K-demuxing 140 are y1, y2, y3, and y4, referred toas 4 recovered K-muxed data streams which have been digitallyde-enveloped by the 4 de-enveloping processor 126-1 to 126-4. Thesedigital envelopes are from a candidate envelope folder 180. All thepotential envelopes are in the candidate envelope folder 180, and shallbe known to both the source 112 and the destinations 122.

The K-demuxing 140 must perform a transform which is the correspondinginverse transform to that of the K-muxing 130 in FIG. 4A, featuring anorthogonal matrix or a non-orthogonal matrix, as long as the inversematrix exists. The 4 outputs from the K-demuxing 140 shall be therecovered Pbx data stream and 3 recovered information data streams xa,xb and xc, or Sx(t), Sy(t) and Sz(t). The information data streamsSx(t), Sy(t), and Sz(t) intended for a user x in a first, a user y in asecond, and a user z in a third of the 3 destinations 122, are recoveredthrough 3 different linear combinations in 3 individual operations ofK-demuxing 140 in three different destinations 122. The 4 identicalpotential inputs to the 3 individual operations of K-muxing 140 are [y1,y2, y3, y4].

In scenarios with known Pbx at one of 3 destinations 122, the receiverat the destination is required to capture only any 3 of the 4satellite-relayed or satellite-transponded enveloped K-muxed informationstreams ye1, ye2, ye3, ye3, and ye4. Three of the 4 de-envelopingprocessors 126-1 to 126-4 shall de-envelope all three of them,recovering a subset of three from the 4 K-muxed information datastreams; [y1, y2, y3, y4]. Let us assume the 3-y subset is [y1, y3, y4].According to Equations (9-1) to (9-4), the K-demuxing 140 in the firstof 3 destinations 122 shall be configured for solving xa through a firstunique linear combination of 3 components of the 3-y subset [y1, y3,y4]. Similarly, the K-demuxing 140 in the second and the third of the 3destinations 122 shall be configured, respectively, for solving xb andxc individually through a second and third unique linear combinations of3 components of the same 3-y subset; [y1, y3, y4].

The block diagrams in FIG. 4C and FIG. 4D are complementary to eachother in a configuration for enveloping 4 K-muxed information streams bya same formatted envelope. FIG. 4C illustrates a different configurationfrom FIG. 4A; both are more detailed functional blocks at the source 112in FIG. 4 . There are two major concurrent functions in a single block,the K-muxing 130. It features (1) K-muxing of 3 information data streamswith a digital envelope stream and concurrent enveloping of 4 K-muxedinformation streams. Three information data streams Sx(t), Sy(t), andSz(t) are to be sent to, respectively, a user x in a first, a user yin asecond, and a user z in a third of 3 destinations 122. A digitalenvelope stream Ex and the 3 information data streams are connected tothe 4 inputs of a 4-to-4 K-muxing 130. The digital envelope is selectedfrom the candidate envelope folder 180.

Let us assume a 4-to-4 Hadamard transform be the matrix for the K-muxing130. The enveloped K-muxed files ye1, ye2, ye3 and ye4 are the 4 outputsfrom the K-muxing 130. To create camouflaged effects on the 4 outputteddata streams for wireless transport; the original digital envelope Exmust be “heavily weighted” before the K-muxing 130 operation.

As an example, E5 features a Chinese painting of a “running horse” shownin FIG. 1 , and E5(t) in a digital picture format is selected as Exwhich is connected to the first input. Referring to equation (10) whichis repeated below, the 4 inputs [y1, y2, y3, y4] to a 4-to-4 Hadamardtransform are y1=E5 and y2=Sx=xa, y3=Sy=xb, and y4=Sz=xc. The fouroutputs are [ye1, ye2, ye3, ye4]. In order to assure that the E5(t)image of the Chinese horse painting in y1 to be more dominant featuresin the 4 multiplexed outputs as camouflaged, we have emphasized thepixel intensities of y1 via:

$\begin{matrix}{\begin{bmatrix}{{ye}\; 1} \\{{ye}\; 2} \\{{ye}\; 3} \\{{ye}\; 4}\end{bmatrix} = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} \\{+ 1} & {- 1} & {- 1} & {+ 1}\end{bmatrix}\begin{bmatrix}{{am}*y\;\underset{\_}{1}} \\{y\; 2} \\{y\; 3} \\{y\; 4}\end{bmatrix}}} & (10)\end{matrix}$where am>1. Usually the amplification factor “am” is set to be greaterthan 10. It is also assumed the 4 inputs which were re-formatted into apixel lattice have been fully equalized. As a result, the image of“running horse” painted by Xu Baihong becomes dominant among the 4participating inputs and appears on all 4 outputs of the K-muxing 130.The 4 K-muxed data, i.e., ye1, ye1, ye3 and ye4, shall feature a sameappearance of “running horse” with various intensity settings, asdepicted in the 4 digital images on the second row of FIG. 2E. We havedescribed FIG. 2E in details previously.

FIG. 4D illustrates more detailed functional blocks at one of 3destinations 122 in FIG. 4 . It is also a corresponding block diagram ofdata processing functions to those depicted in FIG. 4C. There are twomajor and separate functions in a single block: the function ofde-enveloping and recovering a desired information data stream frommultiple muxed information data streams.

Referring to equation (11) which is repeated in here the 4 inputs to theK-demuxing 140; ye1, ye2, ye3, and ye4 will be digitally de-envelopedand de-aggregated concurrently. The K-demuxing 140 shall perform aninverse transform to a corresponding one in K-muxing 130 in FIG. 4C. Theinverse matrix is also a Hadamard matrix and its transform ischaracterized by:

$\begin{matrix}{\begin{bmatrix}{{am}*y\; 1} \\{y\; 2} \\{y\; 3} \\{y\; 4}\end{bmatrix} = {\begin{bmatrix}{+ 1} & {+ 1} & {+ 1} & {+ 1} \\{+ 1} & {- 1} & {+ 1} & {- 1} \\{+ 1} & {+ 1} & {- 1} & {- 1} \\{+ 1} & {- 1} & {- 1} & {+ 1}\end{bmatrix}\begin{bmatrix}{{ye}\; 1} \\{{ye}\; 2} \\{{ye}\; 3} \\{{ye}\; 4}\end{bmatrix}}} & (11)\end{matrix}$

where [y1, y2, y3, y4]=[E5, xa, xb, xc].

Four outputs from the K-demuxing 140 shall include a recovered digitalenvelope E5, and 3 recovered information data streams xa, xb, and xc. Inthe first of the 3 destinations 122, Sx(t) for user x is recovered via acustomized first linear combination in the K-demuxing 140:Sx(t)=xa=y2=ye1−ye2+ye3−ye4  (11-1)Similarly, in the second of the 3 destinations 122, Sy(t) for user y isrecovered via a customized second linear combination in the K-demuxing140:Sx(t)=xb=y3=y1+ye2−ye3−ye4  (11-2)Concurrently, in the third of the 3 destinations 122, Sz(t) for user zis recovered via a customized second linear combination in theK-demuxing 140:Sx(t)=xc=y4=ye1−ye2−ye3+ye4  (11-2)

An original digital envelope E5(t) from a local envelope folder 180 ineach of the three destinations 122 shall be used for a digitalcomparison 182 to the recovered envelope bit-by-bit for data integritymonitoring via an integrity index Cx.

In another embodiment where Ex is known at a destination, there is oneredundancy in 4 received independent data streams, [ye1, ye2, ye3, ye4],for solving three unknown information data streams [xa, xb, xc]=[Sx(t),Sy(t), Sz(t)]. It can be used for better availability for communicationchannels between a source 112 and three destinations 122.

FIG. 2E is a replicate of FIG. 5 in US patent application publicationNo. 20150032706. There are 12 digital images on three panels. They areresults of a simulation program implemented in Matlab. The four digitalstreams depicted on the top panel 521 are the 4 inputs to equation (10),y2, y3, y4, and y1, where y2=xa, y3=xb, y4=xc, and y1=E5. The 4 outputsof Equation (10) depicted on the middle panel 522 are [ye1, ye2, ye3,ye4]. As shown on their appearances, each of the 4 outputs has beendigital enveloped by a common envelope E5 but with various brightness.

The 4 images on the bottom panel 523 are result of K-demuxing 140characterized by Equation (11). The four inputs to Equation (10) are thedigital streams on the middle panel 522, and corresponding 4 concurrentoutputs are the digital image streams [y1, y2, y3, y4], which equal to[xa, xb, xc, E5] on the bottom panel 523.

Other Embodiments Via FIG. 4

In a different embodiment, referring back to FIG. 4C, only 3 of the 4outputs [ye1, ye2, ye3, ye4] from a source 112 are delivered to three ofthe 4 satellites 030-1 to 030-4. In this embodiment with a configurationof FIG. 4C and FIG. 4D, the receiver in any one of three destinations122 must use the original envelope data stream Ex in order to de-envelopand to recover [xa, xb, xc] through K-demuxing 140 concurrently.

Similarly, with a configuration of FIG. 4C and FIG. 4D, the receiver ina destination 122 must have access of the digital envelope data streamE5 in order to recover [xa, xb, xc] through K-demuxing 140. Withoutaccessing the local envelope data stream, the received 3 muxed streamstogether shall have insufficient information in reconstituting any ofthe 3 original information streams [xa, xb, xc].

In other embodiments of FIG. 4 , FIG. 4A, FIG. 4B, FIG. 4C and FIG. 4D,any satellite links between a source and a destination may be replacedby airborne-platform-based links, cellular links, wireless terrestriallinks, and/or links via cloud.

Embodiment 5

FIG. 5 depicts a block diagram of a satellite communications conceptsimilar to that of FIG. 2 but using a multi-link connectivity onlythrough one satellite for concurrently delivering multiple data streamsto various users. There are three user information data streams Sx, Sy,and Sz in a source 112 being delivered via a connectivity with multiplelinks in a satellite 030 to three individual users x, y, and z at threedifferent destinations 122. The multi-link satellite communicationsconcept through K-muxing over multiple information data streams features(1) improved privacy via digital enveloping and (2) enhancedavailability via information data redundancy. The source 112 and thedestinations 122 are under coverages of the relaying satellite 030. Itis applicable for direct broadcasting satellites services (BSS), fixedsatellite services (FSS), and mobile satellite services (MSS). Themultilink communications concept is applicable to geostationary (GEO)satellites, and non-GEO satellites including satellites in mid-earthorbit (MEO), and in low-earth orbit (LEO). It may also be implementedfor multicasting services using multiple links via terrestrial cloud,satellites and/or unmanned air vehicles (UAVs).

The block diagram in FIG. 5 shows a concept of communications viamultiple links through a satellite between a sender at a source 112 andreceivers at various destinations 122. There are three segmentsincluding (1) a pre-processing at a communications source or a source110; (2) a multiple-link communications channel including thecommunication satellite 030; and (3) post-processing at destinations 122downstream from the communications satellite 030. The information datasets Sx(t), Sy(t), and Sz(t) are, respectively, for users x, y, and z.Respective digital envelopes are selected from a candidate envelope file180 which stores digital envelopes commonly known for a user communitythat both a sender in the source 112 and receivers at variousdestinations 122 belonged to. There are probing signals, Pbx, which willbe incorporated as an input at the source 112 and recovered at variousdestinations 122 for continuously monitoring the “health” of the dynamiccommunications channels.

Preprocessing at the source 112 produces 4 enveloped K-muxed outputsye1, ye2, ye3, and ye4, as depicted in FIG. 5 . After frequencyup-conversion, modulation, proper filtering, and power amplification,the 4 information streams ye1, ye2, ye3, and ye4 are multiplexed by amultiplexer 510 before sent to the satellite 030. The multiplexer 510may feature a FDM function, such as those output multiplexers in manytransponding satellites for accessing various transponders. Themultiplexing may also be implemented in base-band signal processingbefore frequency up-converted to a RF for accessing various time slotsin a broadcasting satellite transponder operated in a mode of singlecarrier. The multiplexer 510 may also perform proper multiplexingfunctions of frequency division, time division, code division,polarization diversity, and/or combinations of all above; for bestutilization of communication asset on the satellite 030.

At a first of the 3 destinations 122 after low-noise amplification,filtering including demultiplexing by a de-multiplexer 520,frequency-conversion, and de-modulation, both de-enveloping andde-aggregating are implemented in a post-processor via K-demuxing toreconstitute original information data stream Sx(t) for user x and thedigital envelope data stream Ex. The de-enveloping is to process 4received enveloped information data streams from ye1, ye2, ye3, and ye4,removing the digital envelopes. The de-aggregating function performs acustomized linear combination on the 4 de-enveloped information streamsrestoring a desired user information data stream Sx, and the probingsignal Pbx.

Similarly, at either a second or a third of the 3 destinations 122, apost processor will reconstitute the digital probing stream Pbx and anoriginal information data stream Sy(t) or Sz(t), respectively.

The satellite 030 may feature multiple transponders in differentfrequency bands at an orbital slot, a regenerative satellite withadvanced capability of on-board de-modulators and re-modulators, orcombinations of both. The transponders from the satellite 030 may referto 4 different transponders in a same physical satellite, or Ntransponders in a first satellite and (4−N) others in a secondsatellite, where N is 1, 2, or 3 for two satellites in the same orbitalslot. It may also be other combinations from more than 2 satellitescollocated in an orbital slot.

The propagation delays shall be equalized to lineup the data frames ofinformation data streams. For 10 Mbps streams, the timing accuracy shallbe in the order of 100 nanoseconds or 10⁻⁷ seconds.

The block diagrams in FIG. 5A and FIG. 5B are complementary to eachother. FIG. 5A illustrates more detailed functional blocks at the source112 in FIG. 5 . There are two major and separate functional blocks; themixing functions of information data stream among 4 inputs via a 4-to-4K-muxing 130, and those of enveloping 116-1 to 116-4. The enveloping116-1 to 116-4 are concurrently carried out by 4 sets of 2-to-2 K-muxerswith functions identical to the enveloping 116 in FIG. 1A. There are twosets of sequential K-muxing operations in FIG. 5A; the K-muxing 130generating 4 aggregated outputs [y1, y2, y3, y4] among four informationdata streams. The four outputs by the K-muxing 130 are the 4 linearcombinations among the inputs of four information data streams; Pbx, Sx,Sy, and Sz. Four outputs feature different aggregations and each is thenfollowed by one of the 4 enveloping processors 116-1 to 116-4 performinga 2-to-2 K-muxing transform under a customized configuration.

The first input of the K-muxing 130 is a probing data stream, Pbx.Information data streams Sx(t), Sy(t) and Sz(t) intended for a user x ina first, a user y in a second, and a user z in a third of the 3destinations 122 are connected to, respectively, last 3 of the 4 inputsof the K-muxing 130.

There are 4 outputs from the function of K-muxing 130; y1, y2, y3, andy4; which shall be referred to as 4 K-muxed data streams are thendigitally enveloped by the 4 enveloping processor 116-1 to 116-4. Theenveloped K-muxed data streams, ye1 to ye4, are then multiplexed beforebeing sent to the 4 satellites 030-1 to 030-4 concurrently afterproperly modulated, frequency converted, filtered, and then poweramplified.

We may set Sx(t)=xa, Sy(t)=xb, and Sz(t)=xz, and then the K-muxing 130is characterized by the identical 4 simultaneous linear equations (8-1)to (8-4). These equations can be written in a matrix form in equation(8). When [W] is a 4×4 Hadamard matrix or any matrix with an existinginverse matrix, the 4 linear equations (8-1) to (8-4) are independent.When [Y] is known and/or available at a destination 122, all 4 unknowncomponents in the [X], or [Pbx, xa, xb, xc] can be solved or calculated.

It is noticed that for other scenarios where the Pbx is known at adestination, the 4 simultaneous linear equations (8) can be written asequation (9-1) to (9-4). When [Y] becomes available from the satellitelink and Pbx is known a priori, there are 4 simultaneous linearequations for all 3 unknown components in the [X]; or xa, xb, and xc.Therefore there is one built-in redundancy in the four components of[Y]. We only need three of the 4 components in [Y] to solve for thethree unknowns; xa, xb, and xc via equations (9-1) to (9-4).

The K-muxing 130 will be via orthogonal matrices or non-orthogonalmatrices, as long as their inverse matrices exist.

In the 4 enveloping processors 116-1 to 116-4, each featuring 2 inputsand two outputs shall perform the identical enveloping transform as thatshown in the function of enveloping 116 with two inputs and two outputsin FIG. 1A. In anyone of the 4 enveloping processors 116-1 to 116-4, oneof the two inputs is a K-muxed data stream (one of y1 to y4) and theother input is a digital envelope stream selected from a candidateenvelope folder 180. The selected envelopes are e1, e2, e3, and e4 forthe enveloping processors 116-1, 114-2, 116-3 and 116-4, respectively.Furthermore only one of its two outputs is sent for a satellitecommunication channel and the other is grounded.

These digital envelopes (e1, e2, e3, and e4) are from a candidateenvelope folder 180. All the potential digital envelopes are collectedin the local candidate envelope folders 180, and shall be known to boththe source 112 and the destination 122. We may choose 4 completelydifferent digital envelopes for all for 4 K-muxed information datastreams; y1, y2, y3, and y4. On the other hand, we may select anidentical envelope for transporting all 4 of them via individualchannels in the satellites 030.

The enveloped streams ye1, ye2, ye3, and ye4 are then individuallymodulated by 4 modulators 028-1 to 028-4, converting the 4 informationdata streams into 4 signal streams or 4 waveform streams and then FDMmultiplexed by the multiplexer 510 before being sent to the satellite030. The multiplexing functions of the multiplex 510 may be implementedinto other conventional formats, such as FDM, TDM, CDM, polarizationdiversity, and/or combinations of all above.

FIG. 5B illustrates more detailed functional blocks at one of the 3destinations 122 in FIG. 5 . It is also a corresponding block diagram ofdata processing functions to those depicted in FIG. 5A. There are twomajor and separate functional blocks; the functions of de-enveloping126-1 to 126-4, and K-demuxing 140.

The enveloped K-muxed data streams, ye1 to ye4, are recovered from thesatellite 030 after low-noise amplified, FDM demuxed by a FDM-demuxer520, frequency converted, properly filtered, and then individuallyde-modulated by 4 demodulators 032-1, 032-2, 032-3, and 032-4.

In the 4 de-enveloping processors 126-1 to 126-4, each featuring 2inputs and two outputs shall perform the identical de-envelopingtransform as those shown in the function of de-enveloping 126 with twoinputs and two outputs in FIG. 1A. In anyone of the 4 de-envelopingprocessors 126-1 to 126-4, one of the two inputs is a recoveredenveloped K-muxed data stream (one of ye1 to ye4) and the other input isa selected digital envelope stream from a local digital envelope folder180. Furthermore only one of the two outputs is sent for K-demuxing 140and the other is grounded.

The 4 inputs to the K-demuxing 140; y1, y2, y3, and y4; referred to as 4recovered K-muxed data streams which have been digitally de-enveloped bythe 4 de-enveloping processor 126-1 to 126-4. These digital envelopesare from a candidate envelope folder 180. All the potential envelopesare in the candidate envelope folder 180, and shall be known a priori toboth the source 112 and the destinations 122.

The K-demuxing 140 must perform a corresponding transform which is aninverse transform to that of the K-muxing 130 in FIG. 5A, featuringeither an orthogonal matrix or a non-orthogonal matrix, as long as theirinverse matrices exist.

The 4 outputs from a K-demuxing 140 shall be the recovered the Pbx datastream and 3 recovered information data streams xa, xb and xc; or Sx(t),Sy(t) and Sz(t). The information data streams Sx(t), Sy(t), and Sz(t)intended for user x in a first, user y in a second, and user z in athird of the 3 destinations 122, are recovered through 3 differentlinear combinations in 3 individual operations of K-demuxing 140 inthree different destinations 122. The 4 identical potential inputs tothe 3 individual operations of K-muxing 140 are [y1, y2, and y3, andy4].

In scenarios with known Pbx at one of 3 destinations 122, the receiverat the destination requires to capture only any 3 of the 4satellite-relayed or satellite-transponded enveloped K-muxed informationstreams; ye1, ye2, ye3, and ye4. Three of the 4 de-enveloping processors126-1 to 126-4 shall de-envelope all three of them, recovering a subsetof three from the 4 K-muxed information data streams; [y1, y2, y3, y4].Let us assume the 3-y subset is [y1, y3, y4]. According to Equations(9-1) to (9-4), the K-demuxing 140 in the first of 3 destinations 122shall be configured for solving xa through a first unique linearcombination of 3 components of the 3-y subset; [y1, y3, y4]. Similarly,the K-demuxing 140 in the second and the third of the 3 destinations 122shall be configured, respectively, for solving xb and xc individuallythrough a second and third unique linear combinations of 3 components ofthe same 3-y subset; [y1, y3, y4].

In other embodiments, the two cascaded K-muxing functions of dataaggregating (or mixing) and enveloping in FIG. 5A can be implemented byone-K-muxing concurrently similar to the block diagram in FIG. 4C.Similarly, the two cascaded K-demuxing functions of data de-aggregating(or mixing) and de-enveloping in FIG. 5B may be implemented byone-K-demuxing concurrently similar to the block diagram in FIG. 4D.

Additional Comments

The components, steps, features, benefits and advantages that have beendiscussed are merely illustrative. None of them, nor the discussionsrelating to them, are intended to limit the scope of protection in anyway. Numerous other embodiments are also contemplated. These includeembodiments that have fewer, additional, and/or different components,steps, features, benefits and advantages. These also include embodimentsin which the components and/or steps are arranged and/or ordereddifferently.

Unless otherwise stated, all measurements, values, ratings, positions,magnitudes, sizes, and other specifications that are set forth in thisspecification, including in the claims that follow, are approximate, notexact. They are intended to have a reasonable range that is consistentwith the functions to which they relate and with what is customary inthe art to which they pertain. Furthermore, unless stated otherwise, thenumerical ranges provided are intended to be inclusive of the statedlower and upper values. Moreover, unless stated otherwise, all materialselections and numerical values are representative of preferredembodiments and other ranges and/or materials may be used.

The scope of protection is limited solely by the claims, and such scopeis intended and should be interpreted to be as broad as is consistentwith the ordinary meaning of the language that is used in the claimswhen interpreted in light of this specification and the prosecutionhistory that follows, and to encompass all structural and functionalequivalents thereof.

What is claimed is:
 1. A communications system between a source and adestination comprising a transmitter at the source and a communicationconnectivity, the transmitter comprising: a candidate envelope folderconfigured to provide M digital envelopes, M being an integer greaterthan or equal to 1, the M digital envelopes being known a priori datafiles; and a preprocessor having N input ports and N output ports, Nbeing an integer greater than M, configured to perform at least onewavefront multiplexing (WFM) transform on N inputs received at the Ninput ports to generate N outputs at the N output ports, wherein thepreprocessor performs the at least one WFM transform by calculating, foreach of the N outputs, a linear combination of the N inputs using atleast one of the M digital envelopes such that a digital format of afirst output of the N outputs appears to human sensors as havingfeatures substantially identical to a digital format of the at least oneof the M digital envelopes.
 2. The communications system of claim 1,wherein the preprocessor comprises: a first WFM processor having the Ninput ports and N first output ports, configured to perform a first WFMtransform on the N inputs and generate N first outputs at the N firstoutput ports; and a set of second WFM processors coupled to the firstWFM processor to receive the N first outputs respectively, each of thesecond WFM processors being configured to perform a respective secondWFM transform on a respective one of the N first outputs and one of theM digital envelopes and generate a respective enveloped data stream asone of the N outputs.
 3. The communications system of claim 1, whereinthe N inputs include a first input stream for an embedded digitalinformation data file, and a second input stream for one of the Mdigital envelopes.
 4. The communications system of claim 3, wherein thefirst output includes an enveloped data stream which is a weighted sumof the first and the second input streams.
 5. The communications systemof claim 1, wherein the at least one WFM transform includes amagnification factor greater than 1 for at least one of the M digitalenvelopes.
 6. The communications system of claim 5, wherein at least oneof the M digital envelopes is known by a user at the destination.
 7. Thecommunications system of claim 1, wherein the communication connectivityincludes one or more satellite links to one or more satellitetransponders located on one or more satellites.
 8. The communicationssystem of claim 1, wherein the communication connectivity includes linkstransponded by air platforms.
 9. The communications system of claim 1,wherein the communication connectivity includes terrestrial linksthrough IP cloud.
 10. The communications system of claim 1, wherein theat least one WFM transform is performed using an orthogonal matrix. 11.The communications system of claim 1, wherein the at least one WFMtransform is performed using a Hadamard matrix.
 12. The communicationssystem of claim 1, wherein one of the N inputs is a probing data stream.13. A communications system between a source and a destinationcomprising a receiver in the destination and a communicationconnectivity, the receiver comprising: a post-processor having N inputports and N output ports, N being an integer greater than 1, andconfigured to perform a de-enveloping transform on N inputs received atthe N input ports to generate N outputs at the N output ports, the Ninputs including an enveloped data stream of an original input stream;and a candidate envelope folder configured to provide M digitalenvelopes for the de-enveloping transform, M being an integer greaterthan or equal to 1, the M digital envelopes being known a priori datafiles; wherein the post-processor performs the de-enveloping transformby calculating a linear combination of the N inputs using at least oneof the M digital envelopes such that a first output of the N outputs issubstantially identical to the original input stream.
 14. Thecommunications system of claim 13, wherein the postprocessor comprises:a set of N first wavefront demultiplexing (WFD) processors, each of thefirst WFD processors being configured to receive a respective one of theN inputs and one of the M digital envelopes, perform a respective firstWFD transform on the respective one of the N first outputs and the oneof the M digital envelopes and generate a respective de-enveloped datastream; and a second WFD processor coupled to the N first WFDprocessors, configured to receive the respective de-enveloped datastreams, perform a second WFD transform on the respective de-envelopeddata streams and generate the N outputs at the N output ports.
 15. Thecommunications system of claim 13 wherein the N inputs include a firstinput stream for the enveloped data stream, and a second input streamfor the at least one of the M digital envelopes.
 16. The communicationssystem of claim 15 wherein the first output is a weighted sum of thefirst and the second input streams.
 17. The communications system ofclaim 15 wherein the de-enveloping transform includes a magnificationfactor greater than 1 for the at least one of the M digital envelopes.18. The communications system of claim 13 wherein the N inputs includetwo received streams from two relay links.
 19. The communications systemof claim 13 wherein the de-enveloping transform includes a Hadamardmatrix.
 20. The communications system of claim 13 wherein thecommunication connectivity includes one or more satellite links to oneor more satellite transponders located on one or more satellites.